I was reading through a 1960s book of etiquette and this little fact was in there and it seemed interesting but also somewhat suspect. The title pretty much says it all but essentially was doffing a hat a continuation of knights having to raise their helmet visors to talk properly? Personally I'd have thought that helmet visors went out of fashion too far before the right sort of hats and caps were commonplace.
I can't speak to sources, but the popularization of this idea is probably due to Erwin Panofsky, in his classic introduction to the iconological method in art history: "This form of salute [the lifting of one's hat] is peculiar to the western world and is a residue of mediaeval chivalry: armed men used to remove their helmets to make clear their peaceful intentions and their confidence in the peaceful intentions of others," Studies in Iconology (Boulder, Westview, 1972 [1939]), p. 4. Given his massive erudition and expertise in the period, there is probably good reason to believe this.
I heard that this gesture is (also) the origin of the military salute. Can anyone confirm this?
In the Royal Navy subordinates would take their hat off to superiors, based on the usual civilian courtesies of the time, "uncovering" as a sign of respect to a social superior. However, as with many things, change over time meant that rather than taking the hat off completely, the subordinate would merely lift the hat, then this became a touch of the hat, to represent the hat being removed. The touching of the hat became the Naval salute.